Asymptotic Redundancies for Universal Quantum Coding
Abstract
We investigate the question of whether or not there exists a noncommutative/ quantum extension of a recent (commutative probabilistic) result of Clarke and Barron. They demonstrated that the Jeffreys' invariant prior of Bayesian theory yields the common asymptotic (minimax and maximin) redundancy  the excess of the encoding cost over the source entropy  of universal data compression in a parametric setting. We study certain probability distributions for the twolevel quantum systems. We are able to compute exact formulas for the corresponding redundancies, for which we find the asymptotic limits. These results are very suggestive and do indeed point towards a possible quantum extension of the result of Clarke and Barron.
 Publication:

arXiv eprints
 Pub Date:
 December 1996
 DOI:
 10.48550/arXiv.quantph/9612043
 arXiv:
 arXiv:quantph/9612043
 Bibcode:
 1996quant.ph.12043K
 Keywords:

 Quantum Physics
 EPrint:
 35 pages, AmSLaTeX v1.2, with psfig.sty, two postscript figures (fig2.eps, fig3.eps). This is a substantial revision of the previous version. The introduction was rewritten completely. The minimax redundancy problem is now resolved as well